Decompose the followng relations into a set of equivalent BCNF relations.

*The bolded letters are underlined in the problem (candidate key(s)).

1. R(A,B,C,D) where A -> B,C,D and B -> C,D

2. R(A,B,C,D) where A,B -> C,D and B -> D

3. R(A,B,C,D,E) WHERE B,C -> E AND A,B,C -> D,E

4. R(A,B,C,D) WHERE A -> B AND C,D -> A,B

For each of the following relations, normalize it into BCNF, based on the functional dependicies given.

*The bolded text is underlined text in the problem (candidate key(s)).

a. Class (Course_No, Section_No, Room, Capacity)

Room -> Capacity

b. Class (Course_No, Section_No, Course_Name, Room, Capacity)

Room -> Capacity

Course_No -> Course_Name